Godement, R., Universite Paris VII, France

Analyse mathematique I
Convergence, fonctions elementaires

2ieme ed. corr. 2001. XX, 458 p. 33 figs. Broche'
3-540-42057-6

Les deux premiers volumes de cet ouvrage sont consacre's aux fonctions dans R ou C, y compris la the'orie e'le'mentaire des se'ries et inte'grales de Fourier et une partie de celle des fonctions holomorphes. L'expose', non strictement line'aire, combine indications historiques et raisonnements rigoureux. Il montre la diversite' des voies d'acce`s aux principaux re'sultats afin de familiariser le lecteur avec les me'thodes de raisonnement et ide'es fondamentales pluto^t qu'avec les techniques de calcul, point de vue utile aussi aux personnes travaillant seules.
Les volumes 3 et 4 traiteront principalement des fonctions analytiques (the'orie de Cauchy, the'orie analytique des nombres et fonctions modulaires), ainsi que du calcul diffe'rentiel sur les varie'te's, avec un court expose' de l'inte'grale de Lebesgue, en suivant d'assez pre`s le ce'le`bre cours donne' longtemps par l'auteur a` l'Universite' Paris 7.
On reconnai^tra dans ce nouvel ouvrage le style inimitable de l'auteur, et pas seulement par son refus de l'e'criture condense'e en usage dans de nombreux manuels.

Keywords: convergence, derivee, integrale, fonction analytique

Contents: Vol. 1: Convergence, fonctions e'le'mentaires.- Vol. 2: Calcul diffe'rentiel et inte'gral, se'ries de Fourier, fonctions holomorphes.- Vol. 3: Fonctions analytiques, inte'gration, transformation de Fourier.
Les deux premiers volumes de cet ouvrage sont consacre's aux fonctions dans R ou C, y compris la the'orie e'le'mentaire des se'ries et inte'grales de Fourier et une partie de celle des fonctions holomorphes. L'expose', non strictement line'aire, combine indications historiques et raisonnements rigoureux. Il montre la diversite' des voies d'acce`s aux principaux re'sultats afin de familiariser le lecteur avec les me'thodes de raisonnement et ide'es fondamentales pluto^t qu'avec les techniques de calcul, point de vue utile aussi aux personnes travaillant seules.
Le volume 3 traitera principalement des fonctions analytiques (the'orie de Cauchy, the'orie analytique des nombres et fonctions modulaires), ainsi que du calcul diffe'rentiel sur les varie'te's, avec un court expose' de l'inte'grale de Lebesgue, en suivant d'assez pre`s le ce'le`bre cours donne' longtemps par l'auteur a` l'Universite' Paris 7.
On reconnai^tra dans ce nouvel ouvrage le style inimitable de l'auteur, et pas seulement par son refus de l'e'criture condense'e en usage dans de nombreux manuels.
La table des matie`res de'taille' est disponsible sur le serveur de Springer. Voir le catalogue sous: http://www.springer.de

Harrell, F.E., University of Virginia, Charlottesville, VA, USA

Regression Modeling Strategies
With Applications to Linear Models, Logistic Regression, and Survival Analysis

2001. Approx. 600 pp. Hardcover
0-387-95232-2

Many texts are excellent sources of knowledge about individual statistical tools, but the art of data analysis is about choosing and using multiple tools. Instead of presenting isolated techniques, this text emphasizes problem solving strategies that address the many issues arising when developing multivariable models using real data and not standard textbook examples. It includes imputation methods for dealing with missing data effectively, methods for dealing with nonlinear relationships and for making the estimation of transformations a formal part of the modeling process, methods for dealing with "too many variables to analyze and not enough observations," and powerful model validation techniques based on the bootstrap. This text realistically deals with model uncertainty and its effects on inference to achieve "safe data mining".

Keywords: Regression analysis, Survival analysis

Contents: General Aspects of Fitting Regression Models.- Missing Data.- Multivariate Modeling Strategies.- Resampling, Validating, Describing, and Simplifying the Model.- S-PLUS Software.- Case Study in Least Squares Fitting and Interpretation of a Linear Model.- Case Study in Imputation and Data Reduction.- Overview of Maximum Likelihood Estimation.- Binary Logistic Regression.- Logistic Model Case Study 1: Predicting Cause of Death.- Logistic Model Case Study 2: Survival of Titanic Passengers.- Ordinal Logistic Regression.- Case Study in Ordinal Regression, Data Reduction, and Penalization.- Models Using Nonparametic Transformations of X and Y.- Introduction to Survival Analysis.- Parametric Survival Models.- Case Study in Parametric Survival Modeling and Model Approximation.- Cox Proportional Hazards Regression Model.- Case Study in Cox Regression.

Series: Springer Series in Statistics.

Holme, A., University of Bergen, Norway

Geometry
Our Cultural Heritage

2001. Approx. 410 pp. 150 figs. Hardcover
3-540-41949-7

This book contains selected topics from the history of geometry, with "modern" proofs of some of the results, as well as a fully modern treatment of selected basic issues in geometry. The book aims at future teachers of mathematics. All too often the geometry which goes into the syllabus for teacher-students presents the material as pedantic and formalistic, suppressing its dynamic character and its role as part of the foundation for our common cultural heritage. The motivation for the book is to open up these aspects of the field. Another motivation is to provide an invitation to mathematics in general. It is an unfortunate fact that today, at a time when mathematics and knowledge of mathematics are more important than ever, phrases like math avoidance and math anxiety are very much in the public vocabulary. An important task is seriously attempting to heal these ills. Thus the book also aims at an informed public, interested in making a new beginning in math.

Keywords: Geometry, algebraic geometry, history of geometry, teaching mathematics

Contents:
Part I. A Cultural Heritage:
Chapter 1. Early Beginnings
Chapter 2. The Great River Civilizations
Chapter 3. Greek and Hellenic Geometry
Chapter 4. Geometry in the Hellenistic Era
Chapter 5. The Geometry of Yesterday and Today
Chapter 6. Geometry and the Real World
Chapter 7. Axiomatic Geometry
Chapter 8. Axiomatic Projective Geometry
Chapter 9. Models for non-Euclidian Geometry
Chapter 10. Making Things Precise
Chapter 11. Projective Space
Chapter 12. Geometry in the Affine and the Projective plane
Chapter 13. Algebraic Curves of Higher Degrees in the Affine Plane
Chapter 14. Higher Geometry in the Projective plane
Chapter 15. Sharpening the Sword of Algebra
Chapter 16. Constructions with Straightedge and Compass
Chapter 17. Fractal Geometry
Chapter 18. Catastrophe Theory

Holevo, A., Russian Academy of Sciences, Moscow, Russia

Statistical Structure of Quantum Theory

2001. IX, 159 pp. Hardcover
3-540-42082-7

New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.

Keywords: quantum statistics, quantum measurement dynamics, quantum measurement, dynamical semigroups .

Contents: From the content: The Standard Statistical Model of Quantum Mechanics.- Statistics of Quantum Measurements.- Evolution of an Open System. Repeated and Continuous Measurement Processes.- Processes in Fock Space.

Series: Lecture Notes in Physics.

Cerrai, S., Universita di Firenze, Italy (Ed.)

Second Order PDE's in Finite and Infinite Dimension
A Probabilistic Approach

2001. IX, 330 pp. Softcover
3-540-42136-X

This book deals with the study of a class of stochastic differential systems having unbounded coefficients, both in finite and in infinite dimension. The attention is focused on the regularity properties of the solutions and on the smoothing effect of the corresponding transition semigroups in the space of bounded and uniformly continuous functions. The application is to the study of the associated Kolmogorov equations, the large time behaviour of the solutions and some stochastic optimal control problems. The techniques are from the theory of diffusion processes and from stochastic analysis, but also from the theory of partial differential equations with finitely and infinitely many variables.

Keywords: stochastic partial differential equations, transition semigroups, Kolmogorov equations, invariant measures, stochastic optimal control Mathematics Subject Classification : 35K15, 35J, 35R15, 47A35, 49L20, 60H10, 60H15, 60J35, 93C20

Contents: Introduction.- Part I: Finite dimension. Kolmogorov equations Rd with unbounded coefficients. Asymptotic behaviour of solutions; Analyticity of the semigroup in a degenerate case. Part II: Infinite dimension. Smooth dependence on data for the SPDE: the Lipschitz case. Kolmogorov equations in Hilbert spaces. Smooth dependence on data for the SPDE: the non-Lipschitz case (I). Smooth dependence on data for the SPDE: the non-Lipschitz case (II). Ergodicity. Hamilton-Jacobi-Bellman equations in Hilbert spaces. Application to stochastic optimal control problems. Appendix A: Dissipative mappings. Appendix B: Weakly continuous semigroups. Appendix C: Theorem of contractions depending on parameters.

Series: Lecture Notes in Mathematics.VOL. 1762